scholarly journals Finite Element Method for Linear Multiterm Fractional Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Abdallah A. Badr
Keyword(s):  
Differential Equation ◽  
Finite Element Method ◽  
Finite Element ◽  
Numerical Methods ◽  
Existence And Uniqueness ◽  
The Finite Element Method ◽  
Galerkin Approach ◽  
Uniqueness Of The Solution ◽  
Fractional Differential ◽  
Element Method

We consider the linear multiterm fractional differential equation (fDE). Existence and uniqueness of the solution of such equation are discussed. We apply the finite element method (FEM) to obtain the numerical solution of this equation using Galerkin approach. A comparison, through examples, between our techniques and other previous numerical methods is established.

scholarly journals STRENGTH ANALYSIS OF VARIABLE RIGIDITY SLABS ON ELASTIC SUPPORT WITH VARIABLE SUBGRADE RATIO

2019 ◽  
pp. 201-208
Author(s):  
E. V. Barmekova
Keyword(s):  
Differential Equation ◽  
Finite Element Method ◽  
Finite Element ◽  
Elastic Support ◽  
Strength Analysis ◽  
The Finite Element Method ◽  
Variable Rigidity ◽  
Different Thickness ◽  
Element Method

The paper presents the strength analysis of variable rigidity slabs on elastic support with the variable subgrade ratio. The analysis is based on a solution of the differential equation of the slab flexure using the finite element method. The results are obtained for different slabs on the elastic support. The results are presented for the different thickness of the upper layer of the two-layer slab on the elastic support with the variable subgrade ratio.

Development of software based on NX Open for assessing the reliability of REA designs

2018 ◽  
Author(s):  
С.А. Пименов ◽  
П.П. Зорков
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Methods ◽  
Statistical Modelling ◽  
Probabilistic Methods ◽  
The Finite Element Method ◽  
Random Loading ◽  
Random Load ◽  
Wide Range ◽  
Element Method

Рассматриваются основные алгоритмы и численные методы решения задач оценки надежности конструкций радиоэлектронной аппаратуры. Алгоритмы реализованы в виде расчетного программного обеспечения АРКОН для проведения оценки надежности конструкций в условиях случайного нагружения с применением численных методов: метода конечных элементов и метода статистического моделирования. The paper deals with the development of new software which allows us to use probabilistic methods for evaluating the reliability of CEA designs. The main algorithms and numerical methods for solving problems of reliability assessment of REA structures are considered. The reason for conducting the study was the presence of the lag in development of the program-technical complexes aimed at assessment of the strength reliability in relation to the tasks being solved. At the moment, analytical methods for estimating the probability of failure-free operation have been developed. Their implementation requires the existence of a law for the distribution of random load parameters and the system itself. This method is deprived of the method of statistical modelling with the calculation of stresses using the finite element method. The algorithms are implemented in the form of computational software for assessing the reliability of structures under random loading conditions. To implement this method, an open CAE was chosen — a system with the ability to program its own modules — the NX Open system. The developed software is displayed on the NX panel in the form of a special icon tray Reliability. The developed software is intended for analysis of the strength of reliability of CEA structures with random loading. The software does not have domestic or foreign alternatives. The main advantages are universality (the ability to perform calculations for a wide range of designs, taking into account the statistical nature of the initial data), the reliability of the estimated estimates, confirmed by the use of modern numerical methods: the finite element method and the statistical modelling method.

A Numerical Solution of the Elastohydrodynamic Lubrication Problem Using Finite Elements

1972 ◽  
Vol 14 (4) ◽  
pp. 229-237 ◽  
Author(s):  
C. Taylor ◽  
J. F. O'Callaghan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Elements ◽  
Numerical Solution ◽  
Elastohydrodynamic Lubrication ◽  
The Finite Element Method ◽  
Galerkin Approach ◽  
Recent Developments ◽  
Element Method ◽  
Isoparametric Elements

This paper comprises a report on recent developments in the application of the finite element method in the analysis of elastohydrodynamic lubrication (e.h.l.) problems. The basic formulation is effected, using the Galerkin approach and the domain under investigation is discretized using isoparametric elements. The techniques used to locate the inlet and outlet boundaries and those employed during successive iterations are illustrated by application to particular examples.

scholarly journals CONVECTIVE AND RADIATIVE THERMAL TRANSFER WITH MULTIPLE REFLECTIONS: ANALYSIS AND APPROXIMATION BY A FINITE ELEMENT METHOD

2001 ◽  
Vol 11 (02) ◽  
pp. 229-262 ◽  
Author(s):  
J. MONNIER ◽  
J. P. VILA
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Existence And Uniqueness ◽  
Multiple Reflections ◽  
Convection Diffusion ◽  
Thermal Transfer ◽  
Uniqueness Of The Solution ◽  
Nonlinear Integrodifferential System ◽  
Account Heat ◽  
Element Method

We study a 3D steady-state thermal model taking into account heat transfer by convection, diffusion and radiation with multiple reflections (grey bodies). This model is a nonlinear integrodifferential system which we solve numerically by a finite element method. Some results of existence and uniqueness of the solution are proved, the numerical analysis is detailed, error estimates are given and two-dimensional numerical results of thermal exchanges under a car bonnet are presented.

scholarly journals The methods of numerical mechanics for the improvement of machine-tools

2020 ◽  
Vol 10 (2) ◽  
pp. 133-144
Author(s):  
Attila Szilágyi ◽  
Dániel Kiss
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Methods ◽  
General Problem ◽  
Machine Tools ◽  
The Finite Element Method ◽  
Element Method

This paper gives a brief summary on the mechanical and thermal applicability of the finite element method (FEM) from the field of designing procedure of machine tools. The solutions of certain problems, as examples, are also demonstrated. First the summary of such phenomena is performed, where the application of numerical methods is inevitable. Through the brief summary of the general problem of elasticity, the justification of the numerical methods is demonstrated. Finally, examples are set to demonstrate the applicability of the numerical methods and the achieved results, which demonstrate the efficiency of the FEM applied for the development of machine tools. Among several numerical methods the FEM is focused on in this paper.

scholarly journals The implementation of the boundary element method to the Helmholtz equation of acoustics

2021 ◽  
pp. 13-19
Author(s):  
Sergey Sivak ◽  
Mihail Royak ◽  
Ilya Stupakov ◽  
Aleksandr Aleksashin ◽  
Ekaterina Voznjuk
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Element Method ◽  
Numerical Methods ◽  
Helmholtz Equation ◽  
Boundary Value Problems ◽  
Boundary Element ◽  
Three Dimensional ◽  
The Finite Element Method ◽  
Element Method

Introduction: To solve the Helmholtz equation is important for the branches of engineering that require the simulation of wave phenomenon. Numerical methods allow effectiveness’ enhancing of the related computations. Methods: To find a numerical solution of the Helmholtz equation one may apply the boundary element method. Only the surface mesh constructed for the boundary of the three-dimensional domain of interest must be supplied to make the computations possible. This method’s trait makes it possible toconduct numerical experiments in the regions which are external in relation to some Euclidian three-dimensional subdomain bounded in the three-dimensional space. The later also provides the opportunity of not using additional geometric techniques to consider the infinitely distant boundary. However, it’s only possible to use the boundary element methods either for the homogeneous domains or for the domains composed out of adjacent homogeneous subdomains. Results: The implementation of the boundary elementmethod was committed in the program complex named Quasar. The discrepancy between the analytic solution approximation and the numerical results computed through the boundary element method for internal and external boundary value problems was analyzed. The results computed via the finite element method for the model boundary value problems are also provided for the purpose of the comparative analysis done between these two approaches. Practical relevance: The method gives an opportunityto solve the Helmholtz equation in an unbounded region which is a significant advantage over the numerical methods requiring the volume discretization of computational domains in general and over the finite element method in particular. Discussion: It is planned to make a coupling of the two methods for the purpose of providing the opportunity to conduct the computations in the complex regions with unbounded homogeneous subdomain and subdomains with substantial inhomogeneity inside.

Teaching Undergraduate Numerical Methods Through a Practical Multibody Dynamics Project

2011 ◽  
Author(s):  
Alfonso Callejo ◽  
Javier Garci´a de Jalo´n
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Methods ◽  
Multibody Dynamics ◽  
Mechanical Engineering ◽  
Practical Training ◽  
The Finite Element Method ◽  
The Many ◽  
Short Time ◽  
Element Method

Among the many different approaches to teach engineering subjects, the project-based methodology turns out to be one of the most effective ones. In the field of undergraduate numerical methods, it can overcome some of its inherent difficulties. This paper considers a particular context: a general 90-hour numerical methods subject in an Industrial-Mechanical Engineering degree. The methods are applied to mechanical engineering problems such as matrix structural analysis, finite element method, multibody systems (MBS), harmonic analysis, or optimization. The article suggests how an appropriate formulation and a practical MATLAB™-based project make up a good approach for a short-time practical training on multibody dynamics (MBD) within that subject. The keys to the theoretical lessons and an example of the project are explained thoroughly. The mechanical project has to be rich in numerical methods. MBD and the finite element method fulfill this requirement. The former is chosen in this article. The students know the basics, but they have to learn everything about MBD in very little time. This experience can be useful in other educational contexts. After explaining the approach, some sample assignment exercises are described, as well as a possible way to assess the work of the students. The result of this approach is a reasonable achievement-time tradeoff shown in the solid skills acquired by the students and proven by the experience of the last few years.

scholarly journals FINITE ELEMENT METHOD FOR A NONLINEAR DIFFERENTIAL EQUATION DESCRIBING CRYSTAL SURFACE GROWTH

2014 ◽  
Vol 19 (2) ◽  
pp. 155-168 ◽  
Author(s):  
Xiaopeng Zhao ◽  
Fengnan Liu ◽  
Bo Liu
Keyword(s):  
Differential Equation ◽  
Finite Element Method ◽  
Finite Element ◽  
Nonlinear Differential Equation ◽  
Crystal Surface ◽  
Surface Growth ◽  
The Finite Element Method ◽  
Order Error ◽  
Projection Approximation ◽  
Element Method

In this paper, for a nonlinear differential equation describing crystal surface growth, the finite element method is presented. A nice order error estimates is derived by means of a finite element projection approximation.

scholarly journals Analysis of the stressed-strained state of the foundation-shell at interaction with the elastic-plastic medium

2021 ◽  
pp. 105-112
Author(s):  
Maksym Vabishchevich ◽  
Gherman Zatyliuk
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Methods ◽  
Bearing Capacity ◽  
The Finite Element Method ◽  
Plastic Medium ◽  
Soil Base ◽  
Elastic Plastic ◽  
The Impact ◽  
Element Method

On the basis of modern numerical implementations of the finite element method the article presents the justification of the adequacy of the method of solving the problems of structures straining in their contact interaction with the elastic-plastic nonlinear soil medium. Compatible calculations of structures and nonlinear bases, which are described by modern mechanical and soil models within one problem is a significant technical problem. The solution of the assigned tasks is possible only within the framework of numerical methods, the most common of which is the finite element method (FEM). The construction of the computational finite element model raises many complex questions that require additional detailed study. In addition, the compliance with the state building norms and regulations is an important factor for further practical use. The use of numerical methods in the calculation of machines and structures, taking into account their interaction with the elastic-plastic medium is largely determined by the complexity or even impossibility of analytical calculation due to the complexity of structural schemes, heterogeneity of material features, uneven soil layers, implementation of step-by-step work execution technologies and so on. The combination of the latest achievements in the field of structural mechanics and soil mechanics is a promising direction for the development of effective approaches to building discrete models of space systems “structure-nonlinear base” for solving applied problems. The use of the developed method allows to significantly specify the structures stress state interacting with the soil base, and to significantly specify the impact on the calculated level of the base bearing capacity. Only the simultaneous consideration of the nonlinear resistance of the soil base together with the plasticity and the structure destruction in the numerical simulation of the foundation-shell load provided good agreement with the natural experiment data as to the type of the boundary state and the bearing capacity level.

scholarly journals The accuracy of numerical methods for the analysis of electrostatic fields

2021 ◽  
Vol 7 (1) ◽  
pp. 59-70
Author(s):  
Vladimir N. Taran ◽  
Maxim V. Shevlyugin ◽  
Aleksey V. Shandybin
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Methods ◽  
Analytical Solution ◽  
Electromagnetic Fields ◽  
The Finite Element Method ◽  
Electrostatic Fields ◽  
Improve Accuracy ◽  
Real Objects ◽  
Element Method

Aim: Estimation of the accuracy of the numerical method relative to the analytical solution. Methods: This article reports on studies of the accuracy of numerical calculations based on the finite element method. The variational scheme of the method is considered. Results: The dependences of errors on the number of simplexes used are obtained and analyzed. The authors noted ways to further improve accuracy. Conclusion: The article gives recommendations on the possible application of the finite element method in solving problems of calculating the electromagnetic fields of real objects.

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